Solutions for End-of-Chapter Questions and Problems: Chapter 17 Part B
11.
Define each of the following four measures of liquidity risk. Explain how each measure
would be implemented and utilized by a DI.
a. Sources and uses of liquidity.
This statement identifies the total sources of liquidity as the amount of cash-type assets that
can be sold with little price risk and at low cost, the amount of funds it can borrow in the
money/purchased funds market, and any excess cash reserves over the necessary reserve
requirements. The statement also identifies the amount of each category the DI has utilized.
The difference is the amount of liquidity available for the bank. This amount can be tracked
on a day-to-day basis.
b. Peer group ratio comparisons
DIs can easily compare their liquidity with peer group institutions by looking at several
easy to calculate ratios. High levels of the loan to deposit and borrowed funds to total asset
ratios will identify reliance on borrowed funds markets, while heavy amounts of loan
commitments to assets may reflect a heavy amount of potential liquidity need in the future.
c. Liquidity index.
The liquidity index measures the amount of potential losses suffered by a DI from a firesale of assets compared to a fair market value established under the conditions of normal
sale. The lower is the index, the less liquidity the DI has on its balance sheet. The index
should always be a value between 0 and 1.
d. Financing gap
The financing gap can be defined as average loans minus average deposits, or alternatively,
as negative liquid assets plus borrowed funds. A negative financing gap implies that the DI
must borrow funds or rely on liquid assets to fund the non-liquid assets.
12.
A DI has $10 million in T-Bills, a $5 million line of credit to borrow in the repo market,
and $5 million in excess cash reserves (above reserve requirements) with the Fed. The DI
currently has borrowed $6 million in fed funds and $2 million from the Fed discount
window to meet seasonal demands.
a. What is the DI’s total available (sources of) liquidity?
The DI’s available resources for liquidity purposes are $10 + $5 + $5 = $20 million.
b. What is the DI’s current total uses of liquidity?
The DI’s current use of liquidity is $6 + $2 = $8 million.
17-1
c. What is the net liquidity of the DI?
The DI’s net liquidity is $12 million.
d. What conclusions can you derive from the result?
The net liquidity of $12 million suggests that the DI can withstand unexpected withdrawals
of $12 million without having to reduce its less liquid assets at fire-sale prices.
13.
A DI has the following assets in its portfolio: $20 million in cash reserves with the Fed,
$20 million in T-Bills, and $50 million in mortgage loans. If the assets need to be
liquidated at short notice, the DI will receive only 99 percent of the fair market value of the
T-Bills and 90 percent of the fair market value of the mortgage loans. Estimate the liquidity
index using the above information.
n
i
I = ∑ wi P
*
Pi
i
where wi = weights of the portfolio,
Pi = fire-sale prices,
Pi* = fair market value of assets
Thus, and assuming that fixed assets will not be disposed on short notice:
I = ($20m/$90m)(1.00/1.00) + ($20m/$90m)(0.99/1.00) + ($50m/$90m)(0.90/1.00)
= 0.942
14.
Conglomerate Corporation has acquired Acme Corporation. To help finance the takeover,
Conglomerate will liquidate the overfunded portion of Acme’s pension fund. The face
values and current and one-year future liquidation values of the assets that will be
liquidated are given below:
Liquidation Values
Asset
Face Value
t=0
t=1
IBM stock
$10,000
$9,900
$10,500
GE bonds
$5,000
$4,000
$4,500
Treasury securities
$15,000
$13,000
$14,000
Calculate the 1-year liquidity index for these securities.
n
i
I = ∑ wi P
*
Pi
i
where wi = weights of the portfolio,
Pi = fire-sale prices,
Pi* = fair market value of assets
Thus,
I = ($10,000/$30,000)($9,900/$10,500) + ($5,000/$30,000)($4,000/$4,500) +
($15,000/$30,000)($13,000/$14,000) = 0.927
15.
Plainbank has $10 million in cash and equivalents, $30 million in loans, and $15 in core
deposits.
17-2
a. Calculate the financing gap.
Financing gap = average loans – average deposits = $30 million - $15 million = $15 million
b. How can the financing gap be used in the day-to-day liquidity management of the
bank?
A rising financing gap on a daily basis over a period of time may indicate future liquidity
problems due to increased deposit withdrawals and/or increased exercise of loan
commitments. Sophisticated lenders in the money markets may be concerned about these
trends and they may react be imposing higher risk premiums for borrowed funds or stricter
credit limits on the amount of funds lent.
17.
What is a bank run? What are some possible withdrawal shocks that could initiate a bank
run? What feature of the demand deposit contract provides deposit withdrawal momentum
that can result in a bank run?
A bank run is an unexpected increase in deposit withdrawals from a bank. Bank runs can be
triggered by several economic events including (a) concern’s about solvency relative to other
banks, (b) failure of related banks, and (c) sudden changes in investor preferences regarding the
holding of nonbank financial assets. The first come, first serve (full pay or no pay) nature of a
demand deposit contract encourages priority positions in any line for payment of deposit
accounts. Thus, even though money may not be needed, customers have incentive to withdraw
their funds.
18.
The following is the balance sheet of a DI in millions:
Assets
Cash
Loans
Plant and equipment
Total
$ 2
$50
$ 3
$55
Liabilities and Equity
Demand deposits
$50
Equity
Total
$ 5
$55
The asset-liability management committee has estimated that the loans, whose average
interest rate is 6 percent and whose average life is three years, will have to be discounted at
10 percent if they are to be sold in less than two days. If they can be sold in 4 days, they
will have to be discounted at 8 percent. If they can be sold later than a week, the DI will
receive the full market value. Loans are not amortized; that is, principal is paid at maturity.
a. What will be the price received by the DI for the loans if they have to be sold in two
days. In four days?
Price of loan = PVAn=3,k=10($3m) + PVn=3, k=10($50m) = $45.03m if sold in two days.
Price of loan = PVAn=3,k=8($3m) + PVn=3, k=8($50m) = $47.42m if sold in four days.
b. In a crisis, if depositors all demand payment on the first day, what amount will they
receive? What will they receive if they demand to be paid within the week? Assume no
deposit insurance.
17-3
If depositors demand to withdraw all their money on the first day, the DI will have to
dispose of its loans at fire-sale prices of $45.03 million. With its $2 million in cash, it will
be able to pay depositors on a first-come basis until $47.03 million has been withdrawn.
The rest will have to wait until liquidation to share the remaining proceeds.
Similarly, if the run takes place over a four-day period, the DI may have more time to
dispose of its assets. This could generate $47.42 millions. With its $2 million in cash it
would be able to satisfy on a first-come basis withdrawals up to $49.42 million.
19.
What government safeguards are in place to reduce liquidity risk for DIs?
Deposit insurance and the Federal Reserve’s discount window both help in the event of a
liquidity drain and both help to prevent liquidity drains from occurring.
Integrated Mini Case: Measuring Liquidity Risk
A DI has the following balance sheet (in millions).
Assets
Cash
Loans
Securities
Total assets
Liabilities and Equity
Deposits
Purchased funds
Equity
Total Liabilities and Equity
$9
95
26
$130
$75
40
15
$130
The DI’s securities portfolio includes $16 million in T-bills and $10 million in GNMA securities.
The DI has a $20 million line of credit to borrow in the repo market and $5 million in excess
cash reserves (above reserve requirements) with the Fed. The DI currently has borrowed $22
million in Fed funds and $18 million from the Fed discount window to meet seasonal demands.
1. What is the DI’s total available (sources of) liquidity?
The DI’s available resources for liquidity purposes are $16m + $10m + $9m +$20m = $55
million.
2. What is the DI’s current total uses of liquidity?
The DI’s current use of liquidity is $22 + $18 = $40 million.
3. What is the net liquidity of the DI?
The DI’s net liquidity is $55 million - $40 million = $15 million.
4. Calculate the financing gap.
17-4
Financing gap = average loans – average deposits = $95 million - $75 million = $20 million
5. (skip)
6. The DI expects a net deposit drain of $20 million. Show the DI's balance sheet if the
following conditions occur:
a. The DI purchases liabilities to offset this expected drain.
If the DI purchases liabilities, then the new balance sheet is:
Cash
Loans
Securities
$9
95
26
$130
Deposits
Purchased liabilities
Equity
$55
60
15
$130
b. The stored liquidity management method is used to meet the expected drain (the DI
does not want the cash balance to fall below $5 million, and securities can be sold at
their fair value).
If the DI uses reserve asset adjustment, a possible balance sheet may be:
Cash
Loans
Securities
$5
95
10
$110
Deposits
Purchased liabilities
Equity
$55
40
15
$110
7. In the event of an unexpected and severe drain on deposits in the next 3 and 10 days,
the DI will liquidate assets in the following manner:
Asset
Cash
Treasury bills
GNMAs
Loans
Liquidation Values ($ millions)
Fair Value
t=3
t = 10
$ 9
$ 9
$ 9
16
14
15.5
10
8
9
95
65
75
Calculate the 3-day and 10-day liquidity index for the DI.
I3-day = ($9m/$130m)($9m/$9m) + ($16m/$130m)($14m/$16m) +
($10m/$130m)($8m/$10m) + ($95m/$130m)($65m/$95m) = 0.7385
I10-day = ($9m/$130m)($9m/$9m) + ($16m/$130m)($15.5m/$16m) +
($10m/$130m)($9m/$10m) + ($95m/$130m)($75m/$95m) = 0.8346
17-5